Neutron Scattering

Figure 15 .2 :
Elastic and inelastic contribution to the incoherent scattering function for jump
motion between two site . The Figure assumes a jump distance of 1.5Â .
The associated pair conelation function is more difficult to obtain, since now we have to deal
with a change of configurations of atoms rather than with single atom jumps . The conceptual
différence between the pair and the self correlation fonction for jump processes may bc
visualized most easily considering rotational jumps . Let us regard e.g . the 120° rotational
jumps of a methyl group around its symmetry axis. An incoherent study would reveal the
atomic jumps ofthe associated hydrogens. The pair correlation function reflects the change of
atomic configurations before and after the jump . Since a 120° jump does not change the
configuration, a coherent scattering experiment would not reveal anything .
Back to the pair conelation fonction for the ß-process, where we will introduce a simple
approximation . We know that for t = 0 the pair conelation function is reflected by the static
structure factor S(Q) . Therefore for t = 0 the corresponding pair conelation fonction for the ß-
process must reveal SQ . We now assume that the inelastic scattering is related to
uncorrelated jumps of thé différent atoms . Then all interférences for thé inelastic process are
destructive and thé inelastic foret factor should be idenfcal to that of thé self conelation
fonction. For thé normalized dynamic structure factor for thé ß-process we arrive at
S(Q,t) ß - S(Q) -Slnel (Q) + Sinel ( Q ) e 2t/ti(E)\
S l (Q) - (Q) S« )
g (E)
(15 .6)
15-5